Abstract

We consider the situation when the values of the auxiliary variable approximating the study variable observed in the probability sample cover only a part of the survey population. Such auxiliary variables may be available in administrative data or big non-probability samples from alternative sources. Due to the non-representativeness of the latter samples, the naive use of their data as covariates in standard small area estimation models may yield worse results than the direct estimation based only on the probability sample data. We propose methods for integrating incomplete auxiliary data into area-level models when a relationship between the study and auxiliary variables is not necessarily linear. We overview the results of some applications in official statistics.